The use of the three mixed data evaluation techniques described in this paper can be illustrated by means of an application to a housing allocation problem in South-East IJsselmonde, an area near Rotterdam in The Nether- lands. A large part of this area is covered by urban developments, which are to a large extent the result of recent growth in the urban areas. As a conse- quence, the region has many new residential areas and a relative lack of hgh- level services. Many people living in t h s area are, therefore, still dependent on Rotterdam for cultural or educational facilities. Continuation of the current policy might cause massive dislocation in t h s region. The increasing number of commuters will cause tremendous traffic problems when certain capacity lim- its are reached; even now approximately BOO0 people living in the study area a r e employed elsewhere. Limiting the urban sprawl would also be desirable because the open areas left between the cities could then be turned into indus- trial parks. This sort of approach is essential if a balanced urban structure is to be attained.
The above comments suggest that a step-wise development of the remain- ing open area would be desirable. This area is therefore divided into eleven &s- tinct zones, which vary in size from about 20 hectares to 60 hectares. Each zone may contain one single urban (i.e., housing or industrial) function. The purpose of the evaluation is to classify these zones with respect to their suita- bility for industrial or housing development. This suitability is determined using the criteria summarized in Table 2 and described in more detail else- where (Voogd, 1902). Table 2 also presents the evaluation matrix, which shows t h a t some of the criteria are assessed on a cardinal scale, while others are measured on an ordinal scale. If the criterion is such that a high score or large number of crosses represents a favorable outcome, there is a (+) in the final
-
20-
Table 2. The e v a l u a t i ~ n m a t r i x
column; the converse is indicated by a (-).
Table 2 does not immediately suggest any obvious conclusions. None of the zones fully dominates the others, which implies that a 'final ranking' can only be obtained if priorities are assigned. Because there is a different number of subcriteria in each main criteria category it is necessary to adopt a so- called "sector evaluation" approach (see Voogd, 1982). Tlvs means that all zones are first evaluated with respect to each main criteria category separately. A few qualitative sets of weights are given in Table 3. Only two 'ordi- nal' levels are distinguished; the information available does not justify a more detailed priority structure.
The symbol 2 means 'is more or equally preferred to'. The labels used to describe the alternative priority rankings are quite arbitrary: the term 'economic view' is used when the criteria emphasized are important from a financial or broader "cost-benefit" point of view; the term 'social view' is used if the criteria stressed are of some general social importance. Because this
Table 3. Priority r a n k i n g s w i t h i n criteria categories. niques, the rankings themselves will not be explained here.
The evaluation scores of Table 2 and the priorities of Table 3 were then analyzed using the three mixed data techniques (with scaling parameter y
=
I), yielding a number of 'aggregated evaluation matrices'. This simply means that an ordinal appraisal score for each zone was calculated for each priority rank- ing and technique, using the random weights procedure (see Section 4). Two aggregated evaluation matrices are possible: a matrix based on economic priorities and a matrix based on social priorities. These matrices are given in Tables 4 and 5: the elements of the matrices represent rankings, where the lower the value the better the rankmg.Two conclusions may be drawn from these condensed evaluation matrices.
The first is that they are remarkably similar: the same zones come out 'first' in each criteria category in both tables. The second conclusion is that the vari- ous criteria categories yield rather conflicting rankings for some zones. For example, zone 11 is a relatively poor housing location with respect to accessi- bility and agricultural situation, although i t is a relatively good location from the point of view of recreation and the housing environment.
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I t is also possible to draw more straightforward conclusions from Tables 4 Criteria category
tion techniques mentioned earlier. The priority sets used in this evaluation are given in Table 6.
The priorities labelled 'industriz! v i e w ' are used with Table 4 w h l e the priorities labelled 'housing views' are combined with Table 5. I t is found t h a t t h e three mixed data techniques yield different probability matrices P but exactly the same final ranking of the zones (for further information on the pro- babilities, see Voogd, 1982). These results are illustrated in Figure 2. The first four columns give the rankings of the zones for the four priority sets listed in Table 6; the last two columns show the aggregated final rankings when priority is given to industry or housing, respectively
Better
Worse
Industrial Industrial I . I I
10
1
2 6 11
1 4
Housing
I Housing Industrial Housing I I
Figure 2. The f i n a l r a n k i n g s r e s u l t i n g from t h e e v a l u a t i o n of t h e a g g r e g a t e d e v a l u a t i o n m a t r i c e s .
Figure 2 reveals t h a t the differences in priorities between the two indus- trial views and between the two housing views have little effect on the final rankmg of zones. Zone 10 is undoubtedly the most appropriate location from an industrial point of view, given the priorities listed in Table 6. From the hous- ing viewpoint, both zone 10 and zone 5 are very attractive, and for this reason no distinction is made between these zones in the last colurnn of Figure 2. Zone
1 is undoubtedly much more suitable for housing than for industrial develop- ment, while the opposite is true of zones 7 and 8. The other zones have similar rankings for both functions, and could be regarded as equally suited to either.
However, Figure 2 shows that zone 4 is not very attractive for either housing or industrial development, and another use for this piece of land should perhaps be considered.